Resistance Element, Its Precursor, and Resistance Value Adjusting Method

ABSTRACT

An object of the invention is to provide a resistor element that makes it possible to adjust the resistance value of a precursor easily in producing a resistance element having a target resistance value from the precursor, as well as to the precursor and a related resistance value adjusting method.  
     A precursor  70  has a meandering resistance pattern formed on a front surface  11  of a substrate  10  as well as at least three trimming lines. The precursor  70  is configured so as to be defined by a geometric sequence that satisfies Inequality 0.5α k &lt;α k+1 &lt;α k , where α k  is the general term of the sequence that is obtained by arranging, in descending order, resistance value increases of the precursor at the time of cutting of the respective trimming lines and normalizing the thus-arranged resistance value increases by an initial resistance value of the precursor in a state that none of the trimming lines are cut.

TECHNICAL FIELD

The present invention relates to a resistance element, its precursor,and a resistance value adjusting method.

BACKGROUND ART

As disclosed in the following Patent document 1, for example, aprecursor of a resistance element is known that is applied to athin-film temperature sensor. This precursor of a resistance elementwhich is applied to a thin-film temperature sensor is produced byevaporating a platinum film on an alumina substrate by sputtering andpatterning the platinum film into a prescribed pattern byphotolithography.

Patent document 1: Japanese Utility Model Application Laid-Open No. Sho63-187303

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

Incidentally, in the precursor of a resistance element which is producedin the above-described manner, the prescribed pattern is formed in sucha manner that plural resistance adjustment patterns whose resistancevalues are weighted so as to have relative values 2⁰, 2¹, 2², 2³, . . .are arranged in order. To produce a resistance element having a targetresistance value from this precursor, it is necessary to trim theresistance adjustment patterns of the precursor.

However, since as described above the plural resistance adjustmentpatterns are arranged in such a manner that their resistance values areweighted so as to have such relative values as to provide 2^(n)resistance values, in determining trimming portions to be trimmed of theprecursor, the number of combinations of trimming portions and aninitial resistance value, that is, a pre-trimming resistance value ofthe precursor, amounts to an enormous number of 2^(n).

Therefore, in the above precursor, trimming portions to be trimmed needto be determined by using such an enormous number of combinations oftrimming portions and an initial resistance value. This results in aproblem that much time and labor are needed to generate data to be usedfor determining trimming portions and input the generated data.

To solve the above problems, an object of the present invention is toprovide a resistor element that makes it possible to adjust theresistance value of a precursor easily in producing a resistance elementhaving a target resistance value from the precursor, as well as to theprecursor and a related resistance value adjusting method.

Means for Solving the Problems

To solve the above problems, a precursor according the aspect of theinvention recited in claim 1 has a resistance pattern (71) which isformed on a substrate (10) with a resistance material in meandering formand short-circuiting portions (74-79) which are formed so as toshort-circuit plural pairs of longitudinal intermediate portions of theresistance pattern, respectively.

In this precursor, the plural pairs of longitudinal intermediateportions are at least three pairs of longitudinal intermediate portions.

In a normalized resistance value increase sequence obtained byarranging, in descending order, resistance value increases at the timeof cutting of the respective short-circuiting portions and normalizingthe resistance value increases by a resistance value obtained in a statethat none of the short-circuiting portions are cut, a smaller one ofeach adjoining pair of normalized resistance value increases of thenormalized resistance value increase sequence is larger than ½ of alarger one.

A normalized resistance value increase ratio of a larger one of eachadjoining pair of normalized resistance value increases of thenormalized resistance value increase sequence to a smaller one is aconstant value.

Producing a precursor in the above-described manner makes it possible toprovide a precursor for a resistance element whose resistance value caneasily be adjusted to a target resistance value.

In the precursor according to the aspect of the invention recited inclaim 1, the normalized resistance value increase sequence is a sequencehaving terms α_(k)'s (k=1, 2, 3, . . . ) and satisfies0.5α_(k)<α_(k+1)<αk.

This sequence may be a geometric sequence whose common ratio is theabove constant normalized resistance value increase ratio.

A precursor according the aspect of the invention recited in claim 2 hasa resistance pattern (71) which is formed on a substrate (10) with aresistance material in meandering form and short-circuiting portions(74-79) which are formed so as to short-circuit plural pairs oflongitudinal intermediate portions of the resistance pattern,respectively.

In this precursor, a normalized resistance value increase sequenceobtained by arranging, in descending order, resistance value increasesat the time of cutting of the respective short-circuiting portions andnormalizing the resistance value increases by a resistance valueobtained in a state that none of the short-circuiting portions are cutis a sequence which has terms α_(k)'s (k=1, 2, 3, . . . ) and satisfies(1+α₁+α₂+ . . . +α_(k))(1+α_(k))=(1+α₁)².

As in the case of the aspect of the invention recited in claim 1,producing a precursor in the above-described manner makes it possible toprovide a precursor for a resistance element whose resistance value caneasily be adjusted to a target resistance value.

In a precursor resistance value adjusting method according to the aspectof the invention recited in claim 3, a precursor having a resistancepattern (71) which is formed on a substrate (10) with a resistancematerial in meandering form and short-circuiting portions (74-79) whichare formed so as to short-circuit plural pairs of longitudinalintermediate portions of the resistance pattern, respectively, isprepared and a resistance value of the precursor is adjusted to a targetresistance value by selectively cutting the short-circuiting portions.

In this precursor resistance value adjusting method, the precursor isprepared as a precursor (70) in which the plural pairs of longitudinalintermediate portions are at least three pairs of longitudinalintermediate portions, and a normalized resistance value increasesequence obtained by arranging, in descending order, resistance valueincreases at the time of cutting of the respective short-circuitingportions and normalizing the resistance value increases by a resistancevalue obtained in a state that none of the short-circuiting portions arecut is defined as a geometric sequence which has terms α_(k)'s (k=1, 2,3, . . . ) and satisfies 0.5α_(k)<α_(k+1)<α_(k).

The resistance value of the precursor is adjusted to the targetresistance value by repeating, in descending order of thecutting-induced resistance value increases of the short-circuitingportions of the thus-prepared precursor, processing of:

-   -   a first step (230) of judging whether a resistance value of the        precursor before cutting of the short-circuiting portion is        smaller than a threshold value for the short-circuiting portion;    -   a second step (234) of determining that the short-circuiting        portion should be cut, if the first step judges that the        resistance value of the precursor before cutting of the        short-circuiting portion is smaller than the threshold value for        the short-circuiting portion; and    -   a step of judging, at the first step, skipping the second step,        whether the resistance value of the precursor is smaller than a        threshold value for a next short-circuiting portion whose        cutting-induced resistance value increase is largest next to the        cutting-induced resistance value increase of the current        short-circuiting portion, if the first step judges that the        resistance value of the precursor before cutting of the        short-circuiting portion is larger than or equal to the        threshold value for the short-circuiting portion;

while cutting the short-circuiting portion every time the second stepjudges that the short-circuiting portion should be cut, as theprocessing is repeated.

As described above, the resistance value of the precursor is adjusted tothe target resistance value by repeatedly executing, on thethus-prepared precursor, the first step and the second step or the firststep and again the first step (the second step if skipped) of judgingwhether the resistance value of the precursor is smaller than athreshold value for a next short-circuiting portion whosecutting-induced resistance value increase is largest next to thecutting-induced resistance value increase of the currentshort-circuiting portion, while cutting the short-circuiting portionevery time the second step judges that the short-circuiting portionshould be cut, as the above processing is repeated.

As a result, unlike in the conventional case, the resistance value ofthe precursor can easily be adjusted to the target resistance valuewithout the need for an enormous amount of data for cutting of theshort-circuiting portions.

In a precursor resistance value adjusting method according to the aspectof the invention recited in claim 4, a precursor having a resistancepattern (71) which is formed on a substrate (10) with a resistancematerial in meandering form and short-circuiting portions (74-79) whichare formed so as to short-circuit plural pairs of longitudinalintermediate portions of the resistance pattern, respectively, isprepared and a resistance value of the precursor is adjusted to a targetresistance value by selectively cutting the short-circuiting portions.

In this precursor resistance value adjusting method, the precursor isprepared as a precursor in which a normalized resistance value increasesequence obtained by arranging, in descending order, resistance valueincreases at the time of cutting of the respective short-circuitingportions and normalizing the resistance value increases by a resistancevalue obtained in a state that none of the short-circuiting portions arecut is defined as a sequence which has terms α_(k)'s (k=1, 2, 3, . . . )and satisfies (1+α₁+α₂+ . . . +α_(k))(1+α_(k))=(1+α₁)².

The resistance value of the precursor is adjusted to the targetresistance value by repeating, in descending order of thecutting-induced resistance value increases of the short-circuitingportions of the thus-prepared precursor, processing of:

-   -   a first step (230) of judging whether a resistance value of the        precursor before cutting of the short-circuiting portion is        smaller than a threshold value for the short-circuiting portion;    -   a second step (234) of determining that the short-circuiting        portion should be cut, if the first step judges that the        resistance value of the precursor before cutting of the        short-circuiting portion is smaller than the threshold value for        the short-circuiting portion; and    -   a step of judging, at the first step, skipping the second step,        whether the resistance value of the precursor is smaller than a        threshold value for a next short-circuiting portion whose        cutting-induced resistance value increase is largest next to the        cutting-induced resistance value increase of the current        short-circuiting portion, if the first step judges that the        resistance value of the precursor before cutting of the        short-circuiting portion is larger than or equal to the        threshold value for the short-circuiting portion;

while cutting the short-circuiting portion every time the second stepjudges that the short-circuiting portion should be cut, as theprocessing is repeated.

As described above, as in the case of the aspect of the inventionrecited in claim3, the resistance value of the precursor is adjusted tothe target resistance value by repeatedly executing, on thethus-prepared precursor, the first step and the second step or the firststep and again the first step (the second step if skipped) of judgingwhether the resistance value of the precursor is smaller than athreshold value for a next short-circuiting portion whosecutting-induced resistance value increase is largest next to thecutting-induced resistance value increase of the currentshort-circuiting portion, while cutting the short-circuiting portionevery time the second step judges that the short-circuiting portionshould be cut, as the above processing is repeated.

As a result, unlike in the conventional case, even with the precursor ofthe aspect of the invention recited in claim 4 which is different fromthe precursor of the aspect of the invention recited in claim 3, theresistance value of the precursor can easily be adjusted to the targetresistance value without the need for an enormous amount of data forcutting of the short-circuiting portions.

A resistance element according to the aspect of the invention recited inclaim 5 is produced from a precursor by preparing a precursor having aresistance pattern (71) which is formed on a substrate (10) with aresistance material in meandering form and short-circuiting portions(74-79) which are formed so as to short-circuit plural pairs oflongitudinal intermediate portions of the resistance pattern,respectively, and adjusting a resistance value of the precursor to atarget resistance value by selectively cutting the short-circuitingportions.

In this resistance element, the precursor is a precursor (70) in whichthe plural pairs of longitudinal intermediate portions are at leastthree pairs of longitudinal intermediate portions, and a normalizedresistance value increase sequence obtained by arranging, in descendingorder, resistance value increases at the time of cutting of therespective short-circuiting portions and normalizing the resistancevalue increases by a resistance value obtained in a state that none ofthe short-circuiting portions are cut is defined as a geometric sequencewhich has terms α_(k)'s (k=1, 2, 3, . . . ) and satisfies0.5α_(k)<α_(k+1)<α_(k).

The resistance element is produced from the precursor by adjusting theresistance value of the precursor to the target resistance value byrepeating, in descending order of the cutting-induced resistance valueincreases of the short-circuiting portions of the precursor, processingof cutting the short-circuiting portion if the resistance value of theprecursor before cutting of the short-circuiting portion is smaller thana threshold value for the short-circuiting portion, leaving theshort-circuiting portion uncut if the resistance value of the precursorbefore cutting of the short-circuiting portion is larger than or equalto the threshold value for the short-circuiting portion, and, with thecurrent short-circuiting portion left uncut, cutting a nextshort-circuiting portion whose cutting-induced resistance value increaseis largest next to the cutting-induced resistance value of the currentshort-circuiting portion if the resistance value of the precursor beforecutting of the next short-circuiting portion is smaller than a thresholdvalue for the next short-circuiting portion or leaving the nextshort-circuiting portion uncut if the resistance value of the precursorbefore cutting of the next short-circuiting portion is larger than orequal to the threshold value for the next short-circuiting portion.

Producing a resistance element in the above-described manner makes itpossible to easily provide a resistance element which is produced from,for example, the precursor described in the aspect of the inventionrecited in claim 3.

A resistance element according to the aspect of the invention recited inclaim 6 is produced from a precursor by preparing a precursor having aresistance pattern (71) which is formed on a substrate (10) with aresistance material in meandering form and short-circuiting portions(74-79) which are formed so as to short-circuit plural pairs oflongitudinal intermediate portions of the resistance pattern,respectively, and adjusting a resistance value of the precursor to atarget resistance value by selectively cutting the short-circuitingportions.

The precursor is a precursor (70) in which a normalized resistance valueincrease sequence obtained by arranging, in descending order, resistancevalue increases at the time of cutting of the respectiveshort-circuiting portions and normalizing the resistance value increasesby a resistance value obtained in a state that none of theshort-circuiting portions are cut is defined as a sequence which hasterms α_(k)'s (k =1, 2, 3, . . . ) and satisfies (1+α₁+α₂+ . . .+α_(k))(1+α_(k))=(1+α₁)².

The resistance element is produced from the precursor by adjusting theresistance value of the precursor to the target resistance value byrepeating, in descending order of the cutting-induced resistance valueincreases of the short-circuiting portions of the precursor, processingof cutting the short-circuiting portion if the resistance value of theprecursor before cutting of the short-circuiting portion is smaller thana threshold value for the short-circuiting portion, leaving theshort-circuiting portion uncut if the resistance value of the precursorbefore cutting of the short-circuiting portion is larger than or equalto the threshold value for the short-circuiting portion, and, with thecurrent short-circuiting portion left uncut, cutting a nextshort-circuiting portion whose cutting-induced resistance value increaseis largest next to the cutting-induced resistance value of the currentshort-circuiting portion if the resistance value of the precursor beforecutting of the next short-circuiting portion is smaller than a thresholdvalue for the next short-circuiting portion or leaving the nextshort-circuiting portion uncut if the resistance value of the precursorbefore cutting of the next short-circuiting portion is larger than orequal to the threshold value for the next short-circuiting portion.

Producing a resistance element in the above-described manner makes itpossible to easily provide a resistance element which is produced from,for example, the precursor described in the aspect of the inventionrecited in claim 4.

The parenthesized symbols for the above respective means indicatecorresponding relationships with specific means in the embodimentsdescribed later.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of a first embodiment to which the presentinvention is applied.

FIG. 2 is a partially cutaway plan view showing part of a manufacturingprocess of a temperature sensor of FIG. 1.

FIG. 3 is a plan view of a precursor which is used for producing aresistance element of the temperature sensor of FIG. 1.

FIG. 4 is a block diagram of a trimming apparatus for trimming theprecursor of FIG. 3 which is formed on a substrate.

FIG. 5 is part of a flowchart showing the workings of a computer shownin FIG. 4.

FIG. 6 is the remaining part of the flowchart showing the workings ofthe computer shown in FIG. 4.

FIG. 7 is a flowchart which is executed by the computer to trim aprecursor of Comparative Example 1 for the first embodiment.

FIG. 8 is a table showing a resistance variation ratio at the time ofcutting of a trimming portion for α_(k) (k=1 to 10) in Example of andComparative Examples 1 and 2 for the first embodiment.

FIG. 9 is a graph showing a relationship between the post-trimmingresistance value and the initial resistance value of a precursor ofExample of the first embodiment.

FIG. 10 is a graph showing a relationship between the post-trimmingresistance value and the initial resistance value in Comparative Example1 for the embodiment.

FIG. 11 is a graph showing a relationship between the post-trimmingresistance value and the initial resistance value in Comparative Example2 for the first embodiment.

FIG. 12 is a graph showing a relationship between the resistance valueR₁ and the initial resistance value R₀ in a state that a term α₁ of asequence has not been optimized yet in the second embodiment of theinvention.

FIG. 13 is a graph showing how the minimum value R_(1min) of theresistance value R₁ varies with the value of the term α₁ of the sequencein the second embodiment.

FIG. 14 is a graph showing a relationship between the resistance valueR₁ and the initial resistance value R₀ in the second embodiment.

FIG. 15 is a graph showing a relationship between the resistance valueR₂ and the initial resistance value R₀ in a state that the term α₁ ofthe sequence has been optimized but its term α₂ has not been optimizedyet in the second embodiment.

FIG. 16 is a graph showing how the minimum value R_(2min) of theresistance value R₂ varies with the value of the term α₂ of the sequencein a state that the term α₁ of the sequence has been optimized in thesecond embodiment.

FIG. 17 is a graph showing a relationship between the resistance valueR₂ and the initial resistance value R₀ in a state that the terms α₁ andα₂ of the sequence have been optimized in the second embodiment.

FIG. 18 is a table showing a resistance variation ratio at the time ofcutting of a trimming portion for α_(k) (k=1 to 10) in Example of thesecond embodiment.

FIG. 19 is a graph showing a relationship between the post-trimmingresistance value and the initial resistance value in Example of thesecond embodiment.

FIG. 20 is a table showing a resistance variation ratio(s) at the timeof cutting of a trimming portion for α_(k) (k=1 to 10) or for α_(k) andα_(k)±3σ_(k) in Examples 1-5 of and Comparative Examples 1-4 for thethird embodiment of the invention

FIG. 21 is a graph showing a relationship between the post-trimmingresistance value and the initial resistance value in Example 3 of thethird embodiment.

FIG. 22 is a graph showing a relationship between the post-trimmingresistance value and the initial resistance value in Example 4 of thethird embodiment.

FIG. 23 is a graph showing a relationship between the post-trimmingresistance value and the initial resistance value in Example 5 of thethird embodiment.

FIG. 24 is a graph showing a relationship between the post-trimmingresistance value and the initial resistance value in Comparative Example3 for the third embodiment.

FIG. 25 is a graph showing a relationship between the post-trimmingresistance value and the initial resistance value in Comparative Example4 for the third embodiment.

DESCRIPTION OF SYMBOLS

10 . . . Substrate; 70 . . . Precursor; 71 . . . Resistance patterns;74-79 . . . Trimming lines; 102 . . . Computer.

BEST MODE FOR CARRYING OUT THE INVENTION First Embodiment

FIG. 1 shows an example in which the present invention is applied to aplatinum-resistor-type temperature sensor. This temperature sensor isequipped with a substrate 10 which is made of a material havinghigh-purity alumina (Al₂O₃) as the main component (hereinafter alsoreferred to as “high-purity alumina material”). In this embodiment, amaterial containing alumina by 99.9% or more is employed as thehigh-purity alumina material.

This temperature sensor is equipped with a meandering platinum resistor20 and two connection pads 30. The platinum resistor 20 is formed on acentral portion of a front surface 11 of the substrate 10 by a methoddescribed below. The two pads 30 are formed on the front surface 11 ofthe substrate 10 on both sides of the platinum resistor 20 so as to beintegral with the platinum resistor 20.

This temperature sensor is also equipped with a bonding layer 40 and aprotective layer 50. The bonding layer 40 is bonded to the front surface11 of the substrate 10 so as to cover the platinum resistor 20 and thetwo pads 30. The protective layer 50 is laid on the bonding layer 40 toform a layered structure together.

Next, a manufacturing method of the temperature sensor having the aboveconfiguration will be described. First, a substrate made of theabove-mentioned high-purity alumina material is prepared as a substrate10 (see FIG. 2). Then, as shown in FIG. 2, a platinum film 60 is formedon a front surface 11 of the substrate 10 by sputtering platinum (Pt).

Then, a precursor 70 and two pads 30 are formed on the front surface 11of the substrate 10 by patterning the platinum film 60 byphotolithography (see FIG. 3). The precursor 70, from which a platinumresistor 20 is to be produced, is formed between the two pads 30 in ashape shown in FIG. 3 by the above-mentioned patterning.

The structure of the precursor 70 will be described here in detail. Asshown in FIG. 3, the precursor 70 has two meandering resistance patterns71. The two resistance patterns 71 are formed on the front surface 11 ofthe substrate 10 between the two pads 30 so as to meander (i.e.,reciprocate) in the vertical direction and to occupy a top-left regionand a bottom-right region as viewed in FIG. 3. Of the two resistancepatterns 71, the top-left resistance pattern 71 will also be called afirst resistance pattern 71 and the bottom-right resistance pattern willalso be called a second resistance pattern 71.

As shown in FIG. 3, a left-hand horizontal top end portion (as viewed inFIG. 3) of the first resistance pattern 71 is integral with theleft-hand pad 30. On the other hand, as shown in FIG. 3, a right-handhorizontal top end portion (as viewed in FIG. 3) of the secondresistance pattern 71 is integral with the right-hand pad 30. As shownin FIG. 3, a right-hand horizontal top end portion 72 (as viewed in FIG.3) of the first resistance pattern 71 is integral with a right-handvertical top end portion 73 (as viewed in FIG. 3) of the secondresistance pattern 71.

As shown in FIG. 3, the precursor 70 has six trimming lines 74-79, whichare used for adjusting the resistance between the two end portions(connected to the respective pads 30) of the precursor 70 depending onwhether they are cut or not.

Between the left-hand horizontal top end portion and the right-handhorizontal top end portion 72 of the first resistance pattern 71, thetrimming lines 74-79 form a horizontal straight line with five tophorizontal intermediate portions of the first resistance pattern 71 andare integral with the latter. The five top horizontal intermediateportions are called first, second, third, fourth, and fifth tophorizontal intermediate portions from left to right in FIG. 3.

The trimming line 74 is connected to the left-hand horizontal top endportion of the first resistance pattern 71 and the first top horizontalintermediate portion. The trimming line 75 is connected to the first andsecond top horizontal intermediate portions. The trimming line 76 isconnected to the second and third top horizontal intermediate portions.The trimming line 77 is connected to the third and fourth top horizontalintermediate portions. The trimming line 78 is connected to the fourthand fifth top horizontal intermediate portions. The trimming line 79 isconnected to the fifth top horizontal intermediate portion and theright-hand horizontal top end portion 72 of the first resistance pattern71.

In the first embodiment, in general, conditions (hereinafter alsoreferred to as “precursor conditions”) that the precursor of theresistance element 20 should satisfy are set as follows:

(1) The precursor has a meandering resistance pattern which is formed onthe front surface 11 of the substrate 10.

(2) The precursor has at least three trimming lines.

(3) Inequality0.5α_(k)<α_(k+1)<α_(k)   (1)holds where α_(k) is the general term of a sequence of resistance valueincreases of the precursor at the time of cutting of the respectivetrimming lines, the resistance value increases being arranged indescending order and normalized by an initial resistance value of theprecursor (i.e., its resistance value in a state that none of thetrimming lines are cut).

(4) The above sequence is a geometric sequence whose common ratio isgreater than 0.5 and smaller than 1.0 as is understood from Inequality(1).

The precursor 70 which is produced in the above manner by patterningsatisfies the precursor conditions (1) and (2) because it has the tworesistance patterns and six trimming lines which are shaped as shown inFIG. 3.

It is assumed that the resistance patterns satisfy the precursorconditions (3) and (4). That is, it is assumed that Inequality (1) holdsfor a geometric sequence (general term α_(k); k=1, 2, . . . , 6) ofresistance value increases of the precursor 70 at the time of cutting ofthe respective trimming lines 74-79, the resistance value increasesbeing arranged in descending order and normalized by an initialresistance value of the precursor 70 (i.e., its resistance value in astate that none of the trimming lines 74-79 are cut), and that thecommon ratio of the geometric sequence is greater than 0.5 and smallerthan 1.0.

Next, a description will be made of a resistance value adjusting methodfor adjusting the resistance value of the precursor 70 to a targetresistance value (i.e., the resistance value of the platinum resistor20) by trimming the precursor 70, in the substrate 10 on which theprecursor 70 is formed in the above-described manner. The targetresistance value will be hereinafter represented by Ra.

Before the description of the resistance value adjusting method, theconfiguration of a trimming apparatus which is necessary for trimmingthe precursor 70 will be described with reference to FIG. 4. Thistrimming apparatus is equipped with a movable stage 80 and a YAG laser90. The movable stage 80 is supported so as to be movable in an X-axisdirection (right-left direction in FIG. 4) and a Y-axis direction (paperdepth direction in FIG. 4) in a horizontal plane (XY-coordinate plane)in FIG. 4. The above-described substrate 10 is placed on and fixed tothe movable stage 80 with the precursor 70 up.

The YAG laser 90 is disposed above the movable stage 80 and is supportedso as to be movable in the X-axis direction and the Y-axis directionlike the movable stage 80. The YAG laser 90 emits a laser beam from itsbeam outlet toward the movable stage 80.

As shown in FIG. 4, the trimming apparatus is also equipped with aterminal 100, a controller 110, and a resistance meter 120. The terminal100 is composed of input devices 101 such as a keyboard and a mouse, acomputer 102, and a monitor 103. The input devices 101 input necessarydata to the computer 102 in response to input manipulations performedthereon.

The computer 102 runs a computer program which is based on a flowchartshown in FIGS. 5 and 6. During that course, the computer 102 performsprocessing necessary for the control of the movement position of themovable stage 80, the control of the controller 110, the display of themonitor 103, etc. on the basis of input data from the input devices 101,a measured resistance value of the resistance meter 120, and other data.The computer program is stored in a ROM of the computer 102 in advance.

The monitor 103, which is a display device, displays data that aresupplied from the computer 102 under the control of the computer 102.Controlled by the computer 102, the controller 110 drives the YAG laser90 so as to move it in the X-axis direction or the Y-axis direction. Thecontroller 110 also performs a laser beam emission control on the YAGlaser 90 under the control of the computer 102. The resistance meter 120measures a resistance between the two end portions of the precursor 70and outputs it to the computer 102.

The resistance value adjusting method for adjusting the resistance valueof the precursor 70 to a target resistance value Ra by trimming theprecursor 70 using the above-configured trimming apparatus will bedescribed below. As mentioned above, the substrate 10 is placed on andfixed to the movable stage 80 with the precursor 70 up.

If the trimming apparatus is rendered operational at this stage, thecomputer 102 starts running the computer program which is based on theflowchart of FIGS. 5 and 6. Upon the start of the computer program, atstep 200 in FIG. 5, the computer 102 performs initialization processing,whereby threshold values β₁β₂, . . . , β_(n) are input from the inputdevices 101 according to input manipulations performed thereon. In thisembodiment, the suffix n of β_(n) is 6 at the maximum because the sixtrimming lines exist. The threshold values β₁, β₂, . . . , β_(n) arejudgment references for trimming processing on the respective trimminglines 74, 75, 79.

At step 201, drive processing is performed on the movable stage 80. Inthe drive processing, the movable stage 80 is driven so that theprecursor 70 will be located right under the YAG laser 90. As a result,the movable stage 80 is moved so that the precursor will be locatedright under the YAG laser 90.

After the execution of step 201, at step 202 a variable k is cleared to0. At step 203, processing of displaying a monitoring resistance value Ris performed. In this display processing, a current resistance value ofthe precursor 70 is output from the computer 102 to the monitor 103 as amonitoring resistance value R on the basis of a measurement output ofthe resistance meter 120. In response, the monitor 103 displays, as themonitoring resistance value R, the current resistance value of theprecursor 70.

After the performance of the display processing at step 203, it isjudged at the next step 210 whether or not the monitoring resistancevalue R displayed at step 203 is greater than or equal to a pre-trimminglower limit resistance value Rb of the precursor 70 and smaller than thethreshold value β_(n)=β₆. Since as described above the precursor 70 hasthe six trimming lines, it is assumed here that the threshold value fortrimming processing on the sixth trimming line 79 is β_(n)=β₆ which isgreater than any of the other threshold values β₁ to β₅.

If a relationship Rb≦R<β₆ is satisfied, a judgment result “yes” isproduced at step 210. In this case, at the next step 211, “1” is addedto the variable k to update it to 1; that is, k=k+1=1. At step 220, itis judged whether or not a relationship k≦n is satisfied. Since theprecursor 70 has the six trimming lines, the parameter n is equal to 6.

Since k=1 at this stage, the judgment result of step 220 should be“yes.” Then, it is judged at step 230 whether or not a relationshipR_(k−1)<β_(k) is satisfied. Since k=1 at this stage, it is judgedwhether or not a relationship R_(k−1)=R₀<β₁ is satisfied. In thisembodiment, R₀ represents a pre-trimming resistance value (i.e., initialresistance value) of the precursor 70 and β₁ represents the thresholdvalue as the judgment reference for trimming processing on the trimmingline 74.

If the relationship R_(k−1)=R₀<β₁ is not satisfied, a judgment result“no” is produced at step 230. This means that the trimming line 74 neednot be cut, that is, it should be kept as it is. In this case, since k=1at this stage, the variable R_(k)=R₁ is set to Rat step 231. Theparameter R₁ represents a resistance value of the precursor 70 aftercompletion of the trimming processing on the trimming line 74 (actuallythe trimming line 74 is not cut).

The resistance value R₁ is set to the monitoring resistance value R ofthe precursor 70 after the completion of the trimming processing on thetrimming line 74 (R₁=R). After the execution of step 231, processing ofdisplaying the monitoring resistance value R is performed at step 232.That is, the monitor 103 displays the monitoring resistance value R=R₁which is supplied from the computer 102.

On the other hand, if the relationship R_(k−1)=R₀<β₁ is satisfied atstep 230, a judgment result “yes” is produced. In this case, processingof driving the laser 90 is performed at step 233. As a result of thedrive processing, the controller 110 performs a drive control so thatthe beam outlet of the laser 90 will be located right over the trimmingline 74 of the precursor 70. As a result, the laser 90 is moved so thatits beam outlet will be located right over the trimming line 74 of theprecursor 70.

At the next step 234, processing of cutting the kth trimming line isperformed. Since k=1 at this stage, this cutting processing isprocessing of cutting the trimming line 74. In this processing, thelaser 90 emits a laser beam toward the trimming line 74 under thecontrol of the controller 110. The trimming line 74 is thus cut.

After the execution of step 234, the variable R_(k)=R₁ is set to R atstep 235 as is done at step 231. The parameter R₁ represents aresistance value of the precursor 70 after completion of the trimmingprocessing on the trimming line 74 (actually the trimming line 74 iscut). At step 203, the monitor 103 displays the monitoring resistancevalue R (=R_(k)=R₁) that was set at step 235. Then, it is again judgedat step 210 whether or not the relationship R_(b)≦R<β₆ is satisfied. Inthis judgment, the parameter R is equal to the monitoring resistancevalue that was set at step 235 and hence is equal to R₁. If therelationship R_(b)≦R<β₆ is satisfied, a judgment result “yes” isproduced at step 210.

If step 232 has been executed or a judgment result “yes” is produced atstep 210 as described above, “1” is added to the variable k to update itto 2; that is, k=k+1=2. Since k=2≦n=6, a judgment result “yes” isproduced at step 220. In this case, since k=2, it is judged at step 230whether or not a relationship R_(k−1)=R₁<β_(n)=β₂ is satisfied. Theparameter R₁ represents the above-mentioned resistance value (see step232 or step 235) of the precursor 70 after the completion of thetrimming processing on the trimming line 74. The parameter β₂ representsthe threshold value as the judgment reference for trimming processing onthe trimming line 75.

If the relationship R_(k−1)=R₁<β₂ is not satisfied, a judgment result“no” is produced at step 230. This means that the trimming line 75 neednot be cut. In this case, since k=2 at this stage, the variable R_(k)=R₂is set to R at step 232. The parameter R₂ represents a resistance valueof the precursor 70 after completion of the trimming processing on thetrimming line 75 (actually the trimming line 75 is not cut).

The resistance value R₂ is set to the monitoring resistance value R ofthe precursor 70 after the completion of the trimming processing on thetrimming line 75 (R₂=R). After the execution of step 231, processing ofdisplaying the monitoring resistance value R is performed at step 232.That is, the monitor 103 displays the monitoring resistance value R=R₂which is supplied from the computer 102.

On the other hand, if the relationship R_(k−1)=R₁<β₂ is satisfied atstep 230, a judgment result “yes” is produced. In this case, processingof driving the laser 90 is performed at step 233. As a result of thedrive processing, the controller 110 performs a drive control so thatthe beam outlet of the laser 90 will be located right over the trimmingline 75 of the precursor 70. As a result, the laser 90 is moved so thatits beam outlet will be located right over the trimming line 75 of theprecursor 70.

At the next step 234, processing of cutting the k₂th trimming line isperformed. This cutting processing is processing of cutting the trimmingline 75. In this processing, the laser 90 emits a laser beam toward thetrimming line 75 under the control of the controller 110. The trimmingline 75 is thus cut.

After the execution of step 234, the variable R_(k)=R₂ is set to R atstep 235 as is done at step 231. The parameter R₂ represents aresistance value of the precursor 70 after completion of the trimmingprocessing on the trimming line 75 (actually the trimming line 75 iscut). At step 203, the monitor 103 displays the monitoring resistancevalue R (=R_(k)=R₂) that was set at step 235. Then, it is again judgedat step 210 whether or not the relationship R_(b)≦R<β₆ is satisfied. Inthis judgment, the parameter R is equal to the monitoring resistancevalue that was set at step 235 and hence is equal to R₂. If therelationship R_(b)≦R=R₂<β₆ is satisfied, a judgment result “yes” isproduced at step 210.

From this time onward, steps 211 to 232 or steps 211 to 210 (via step230) are executed repeatedly in the same manner as described with thevariable k becoming equal to 6 at step 211 in the last cycle. Whilethese steps are executed repeatedly, trimming processing is performed oneach of the remaining trimming lines 76-79 (each of the trimming lines76-79 is cut or not cut). If “1” is added to the variable k to update itto 7 (k=k+1=7) at step 211 after these steps are executed repeatedly, ajudgment result “no” is produced at step 220.

When the computer program has proceeded to step 210, if the judgmentresult of step 210 is “no,” “1” is added to the variable k to update itat step 212 (see FIG. 6) as is done at step 211 (step 212 is repeated asthe variable k is changed from “0” to “6” ). Every time “1” is added tothe variable k to update it, whether or not the relationship k≦n=6 issatisfied is judged at step 240 as is done at step 220. If a judgmentresult “yes” is produced at step 240, the variable R_(k) is set toR_(k−1.) That is, R₁ is set to R₀ when k=1, R₂ is set to R₁ when k=2,and so forth. When k=6, R₆ is set to R₅. When k=7, a judgment result“no” is produced at step 240.

Pieces of trimming processing are performed on the precursor 70 in theabove-described manner, whereby the resistance value of the precursor 70is adjusted to the target resistance value Ra. The precursor 70 whoseresistance value has thus been adjusted serves as the platinum resistor20.

After the precursor 70 is trimmed in the above-described manner, pastehaving alumina as the main component is screen-printed on the frontsurface 11 of the substrate 10 so as to cover a right-hand portion ofthe left-hand pad 30 (as viewed in FIG. 1) and a left-hand portion ofthe right-hand pad 30 (as viewed in FIG. 1), whereby a paste layer tobecome the bonding layer 40 is formed. Then, a protective layer 50 islaid on the paste layer by pressing. Then, the substrate 10 on which theprotective layer 50 is laid is fired. The manufacture of aplatinum-resistor-type temperature sensor is thus finished. The firingturns the paste layer into the bonding layer 40.

In the thus-manufactured temperature sensor, the platinum resistor 20has the target resistance value Ra because the resistance value of theprecursor 70 has been adjusted in the above-described manner bytrimming.

As mentioned above, the precursor 70 is configured so as to satisfy theprecursor conditions (1)-(4). Since the resistance value of theprecursor 70 is adjusted to the target resistance value by theresistance value adjustment by trimming according to the flowchart ofFIGS. 5 and 6, the resistance value of the precursor 70 can easily beadjusted to the target resistance value without the need for relying onan enormous amount of data as in the conventional case.

Since the computer program which is necessary for the above resistancevalue adjustment is based on the flowchart of FIGS. 5 and 6, thecomputer program can be written easily whereas an enormous amount ofdata as needed in the conventional case is made unnecessary.

To evaluate the resistance value fitting according to the firstembodiment (i.e., the adjustment of the resistance value of theprecursor 70 to a target value), a precursor having substantially thesame structure as the above-described precursor 70 was prepared asExample and precursors of two Comparative Examples (Comparative Example1 and Comparative Example 2) were also prepared.

In the precursor of Example, the common ratio of a geometric sequencehaving a general term α_(k) is set at 0.59. The precursor of Example isconfigured in substantially the same manner as the precursor 70 so as tobe trimmed by the above-described trimming apparatus according to theflowchart of FIGS. 5 and 6.

On the other hand, in the precursor of Comparative Example 1, the commonratio of a geometric sequence having a general term α_(k) is set at0.50. Therefore, the precursor of Comparative Example 1 has a resistancepattern whose resistance values are weighted so as to have a relativevalue sequence of 2^(n) like the precursor disclosed in Japanese UtilityModel Application Laid-Open No. Sho 63-187303. Therefore, the precursorof Comparative Example 1 is trimmed by the above-described trimmingapparatus according to a flowchart of FIG. 7 rather than the flowchartof FIGS. 5 and 6.

In the precursor of Comparative Example 2, the common ratio of ageometric sequence having a general term α_(k) is set at 0.5. Like theprecursor 70, the precursor of Comparative Example 2 is trimmed by theabove-described trimming apparatus according to the flowchart of FIGS. 5and 6. Therefore, the precursor of Comparative Example 2 has the sameresistance pattern as that of Example except for the difference incommon ratio. The variable k takes values 1, 2, . . . , 10 for thegeneral term α_(k), the target resistance value Ra is set at 200Ω, andthe lower limit resistance value Rb is set at 133.33Ω.

First, the precursor of Comparative Example 1 is trimmed in thefollowing manner according to the flowchart of FIG. 7. That is, it isjudged at step 300 whether or not a pre-trimming resistance value (i.e.,monitoring resistance value R) of the precursor of Comparative Example 1satisfies a relationship Rb≦R≦Ra−C, where C is an allowable error of atarget resistance value.

If the relationship Rb≦R≦Ra−C is satisfied, a judgment result “yes” isproduced at step. 300 At the next step 310, processing of determiningtrimming portions (cutting portions) of the precursor of ComparativeExample 1 is performed. This determining processing is performed on thebasis of 2⁸ combinations.

As described below, the number of combinations is enormous. InComparative Example 1, plural resistance adjustment patterns arearranged in such a manner that their resistance values are weighted soas to have such relative values as to provide 2⁸ resistance values.Therefore, in determining trimming portions (i.e., portions to betrimmed) in Comparative Example 1, the number of combinations oftrimming portions and an initial resistance value amounts to 2⁸.

When cutting portions of the precursor of Comparative Example 1 havebeen determined on the basis of the above-mentioned 2⁸ combinations atstep 310, cutting is performed at step 320 for each determination of acutting portion. Cutting is performed by a laser beam emitted from thelaser 90. Like the precursor of the above-mentioned Example, theprecursor of Comparative Example 2 is trimmed according to the flowchartof FIGS. 5 and 6.

The trimming methods of Example and Comparative Examples 1 and 2produced results shown in a table of FIG. 8. In the table of FIG. 8, theterm “resistance variation ratio at the time of cutting of a trimmingportion” means a ratio of a post-cutting resistance value to apre-cutting resistance value (i.e., initial resistance value).

As shown in the table of FIG. 8, in each of Example and ComparativeExamples 1 and 2, the sum of the resistance variation ratios at the timeof cutting of the trimming portions is equal to 0.498. Whereas inComparative Example 1 the number of threshold values is as enormous as2⁸−1=255, in Comparative Example 2 the number of threshold values isonly eight. In Example, the number of threshold values is 10.

FIGS. 9-11 are graphs showing relationships between the pre-trimmingresistance value (i.e., initial resistance value) and the post-trimmingresistance value in Example and Comparative Examples 1 and 2. FIG. 9 isa graph corresponding to Example, FIG. 10 is a graph corresponding toComparative Example 1, and FIG. 11 is a graph corresponding toComparative Example 2.

The comparison between these graphs shows that the resistance value canbe fit into the target range in each of Example and ComparativeExample 1. However, in Comparative Example 1, since 2⁸ combinations areindispensable in determining cutting portions, the number of thresholdvalues is as enormous as 255. Therefore, not only does the flowchart ofFIG. 7 (i.e., a computer program) is complex but also theabove-mentioned enormous number of combinations and hence the enormousnumber of threshold values is needed. As a result, it takes much timeand labor to generate data for trimming of the precursor of ComparativeExample 1.

In contrast, only 10 threshold values are needed in Example. Therefore,not only the flowchart of FIGS. 5 and 6 (i.e., a computer program) issimple but also the number of threshold value is very small and hencedata for trimming of the precursor of Example can be generated easily.

In Comparative Example 2, as is understood from the fact that in thegraph of FIG. 11 the post-trimming resistance value varies to a largeextent with respect to the initial resistance value, the resistancevalue cannot be fit to the target resistance value Ra.

Although the first embodiment is directed to the case that the precursor70 has six trimming lines, the invention is not limited to such a case.As long as it is prerequisite that Inequality (1) be satisfied, it issufficient for the precursor 70 to have at least three trimming lines.

Second Embodiment

Next, a second embodiment of the invention will be described. In thesecond embodiment, in general, the following precursor conditions areset:

(1) As in the case of the first embodiment, the precursor has ameandering resistance pattern which is formed on the front surface 11 ofthe substrate 10.

(2) Unlike in the first embodiment, the precursor has at least twotrimming lines.

(3) As in the case of the first embodiment, Inequality (1) holds for thegeneral term α_(k) of a sequence.

(4) Unlike in the first embodiment, in the second embodiment thesequence is not required to be a geometric sequence. However, thegeneral term α_(k) should satisfy the following Equation (2).$\begin{matrix}{{\left( {1 + {\sum\limits_{i = 1}^{k}\quad\alpha_{i}}} \right)\left( {1 + \alpha_{k}} \right)} = \left( {1 + \alpha_{1}} \right)^{2}} & (2)\end{matrix}$

The grounds of formulation of Equation (2) will be described below withreference to FIGS. 12-17. FIG. 12 shows a relationship between theinitial resistance value R₀ and the resistance value R₁ that is obtainedby performing trimming processing on the first trimming line (i.e., thefirst trimming line is cut or not cut). In this embodiment, the initialresistance value R₀, which is a resistance value before a start of atrimming operation, should satisfy a relationship Rb≦R₀≦Ra. In thisrelationship, the resistance value R₁ is given by two separate linesegments. If a relationship R₀<β₁ (see step 230 in FIG. 5) is satisfied,the first trimming line is cut. On the other hand, if R₀≧β₁, the firsttrimming line is not cut.

As for the minimum value of the resistance value R₁, which depends onthe value of β₁, one of the following two cases occurs. If the initialresistance value R₀ is equal to β₁, the minimum value R_(1min) of R₁=β₁is given by Ra/(1+α₁). If the initial resistance value R₀ is equal toRb, the minimum value R_(1min) of R₁ is given by Rb(1+α₁) under thecondition R₀<β₁.

Therefore, the dependence of the minimum value R_(1min) of theresistance value R₁ on α₁ is as shown in a graph of FIG. 13. As shown inFIG. 13, α₁ takes an optimum value and the minimum value R_(1min) of theresistance value R₁ is at the maximum (see FIG. 14) when a relationshipRa/(1+α₁)=Rb(1+α₁), that is, (1+α₁)²=Ra/Rb, holds.

FIG. 15 shows a relationship between the initial resistance value R₀ andthe resistance value R₂ that is obtained by performing trimmingprocessing on the second trimming line (i.e., the second trimming lineis cut or not cut). In this relationship, the resistance value R₂ isgiven by four separate line segments, the left ends of which are thefollows four points:

a) A point where R₀ is equal to Rb. In this case, the resistance valueR₂ is given by R_(2a)=Rb(1+α₁+α₂)

b) A point where the resistance value R₁ obtained after the firsttrimming line is cut becomes β₂. In this case, the resistance value R₂is given by R_(2b)=β₂=Ra/(1+α₂).

c) A case that the initial resistance value R₀ is equal to β₁. In thiscase, the resistance value R₂ is given by R_(2c)={Ra/(1+α₁)}(1+α₂)

d) A case that the initial resistance value R₀ is equal to β₂ In thiscase, the resistance value R₂ is given by R_(2d)=Ra/(1+α₂).

Substituting (1+α₁)²=Ra/Rb into the above values R_(2a), R_(2b), R_(2c),and R_(2d), we obtainR _(2a) ={Ra/(1+α₁)²}(1+α₁+α₂)=Rb(1+α₁+α₂)R _(2b) =Ra/(1+α₂)=Rb(1+α₁)²/(1+α₂)R _(2c) ={Ra/(1+α₁)}(1+α₂)=Rb(1+α₁)(1+α₂)R _(2d) =Ra/(1+α₂)=Rb(1+α₁)²/(1+α₂).

Since a relationship R_(2a)<R_(2c) holds apparently, the minimum valueR_(2min) of the resistance value R₂ is equal to one ofR _(2a) =R ₀/{(1+α₁+α₂)(1+α₁)² }=Rb/(1+α₁+α₂); andR _(2d) =R ₀/(1+α₂)=Rb(1+α₁)²/(1+α₂)depending on the value of α₂.

FIG. 16 is a graph showing the dependence of the minimum value R2min(i.e., R_(2a) or R_(2d)) of the resistance value R₂ on α₂. As isapparent from FIG. 16, the minimum value R_(2min) of the resistancevalue R₂ has a largest value when R_(2a)=R_(2d), that is,(1+α₂)(1+α₁α₂)=(1+α₁)² (see FIG. 17).

Likewise, the minimum value of the resistance value R_(k) has a largestvalue when Rb(1+α₁+α₂+ . . . +α_(k))=Rb=Ra/(1+α_(k)), that is,${\left( {1 + {\sum\limits_{i = 1}^{k}\quad\alpha_{i}}} \right)\left( {1 + \alpha_{k}} \right)} = {{{Ra}/{Rb}} = {\left( {1 + \alpha_{1}} \right)^{2}.}}$

From the above discussion, it can be said that the resistance pattern ofthe precursor 70 according to the second embodiment satisfies theabove-mentioned Equation (2).

The precursor 70 is required to have n trimming lines, n satisfying arelationship (Ra−C)≦Ra/(1+α_(n)). This is because ifRa/(1+α_(n))<(Ra−C), the resistance value of a precursor whose initialvalue R₀ satisfies a relationship Ra/(1+α_(n))<R₀<(Ra−C) cannot beadjusted by trimming processing so that a relationship (Ra−C)≦R_(n)≦Rais satisfied.

Where n is set in the above-described manner, a range of the initialresistance value R₀ where the relationship (Ra−C)≦R_(n)≦Ra can besatisfied by trimming processing is given by(Ra−C)/(1+S_(n))≦Ra/{(1+S_(n))(1+α_(n))}<R₀≦Ra, where(1+S_(n)=()1+α₁+α₂+ . . . +α_(n))

As for the range of the initial resistance value of a precursor as asubject of trimming, if (Ra−C)/(1+S_(n))≦R₀≦Ra/{(1+S_(n))(1+α_(n))}=Rb,a post-trimming resistance value R_(n) of the precursor can be fit intoa range (Ra−C)≦R_(n)≦Ra/(1+α_(n)) by cutting all the trimming lines.

If Ra/{(1+S_(n))(1+α_(n))}<R₀≦Ra/(1+α_(n)), a post-trimming resistancevalue R_(n) of the precursor can be fit into a target resistance valuerange Ra/(1+α_(n))≦R₀≦Ra.

A precursor 70 produced by patterning in the manner described in thefirst embodiment has the prescribed resistance pattern and six trimminglines (see FIG. 3). Therefore, this precursor 70 satisfies the precursorconditions (1) and (2) of the second embodiment.

It is assumed that the resistance pattern of the precursor 70 accordingto the second embodiment satisfies the precursor condition (3) of thesecond embodiment as in the case of the first embodiment. It is alsoassumed that the resistance pattern of the precursor 70 according to thesecond embodiment is a modified version of that of the precursor 70according to the first embodiment in that the former satisfies theprecursor condition (4) of the second embodiment

If pieces of trimming processing are performed on the thus-configuredprecursor 70 according to the second embodiment in the same manner as inthe first embodiment by using the trimming apparatus by causing thecomputer 102 to run the computer program (see the flowchart of FIGS. 5and 6), the resistance value of the precursor 70 is adjusted to thetarget resistance value Ra. The precursor 70 whose resistance value hasthus been adjusted serves as the platinum resistor 20.

Therefore, the same workings and advantages as attained by the firstembodiment can be attained by using the precursor 70 according to thesecond embodiment.

To evaluate the resistance value fitting according to the secondembodiment, a precursor having substantially the same structure as theprecursor according to the second embodiment was prepared as Example.The same trimming processing as is to be performed on the precursor 70according to the second embodiment was performed on the precursor ofExample. A table of FIG. 18 shows a result of the trimming processing.

As shown in the table of FIG. 18 and the table of FIG. 8 (firstembodiment), the sum of resistance variation ratios at the time ofcutting of the trimming portions is equal to 0.498 in each ofComparative Examples 1 and 2 and Example of the second embodiment.Whereas in Comparative Example 1 the number of threshold values is asenormous as 2⁸−1=255, in Example of the second embodiment the number ofthreshold values is only 10.

FIG. 19 is a graph showing a relationship between the pre-trimmingresistance value (i.e., initial resistance value) and the post-trimmingresistance value in Example of the second embodiment. It is seen fromFIG. 19 that in Example of the second embodiment the resistance valuecan be fit into a target range.

Third Embodiment

FIGS. 20-25 show important features of a third embodiment of theinvention. The third embodiment is different from the first or secondembodiment in that the former is proposed with the following items takeninto consideration.

In the same manner as described in the first or second embodiment,meandering resistance patterns 71 formed on the substrate 10 aredesigned so that resistance variation ratios at the time of cutting oftrimming lines become equal to target values. In designing meanderingresistance patterns 71, it is assumed that the general term α_(k) inInequality (1) or Equation (2) described in the first or secondembodiment has no variation.

However, in actuality, the resistance patterns 71 have variations inwidth and thickness as well as in pattern accuracy. Therefore, thegeneral term α_(k) actually has a variation and hence each of theabove-mentioned resistance variation ratios varies from one resistanceelement to another.

Therefore, since the resistance value can be adjusted only in theincreasing direction in cutting trimming lines in the above-describedmanner, the resistance value may increase beyond a target range bycutting trimming lines if such variations are not taken intoconsideration.

A desirable measure against the above problem is to employ largerresistance variation ratios in determining trimming lines to be cuttaking such variations into consideration or setting a post-trimmingtarget resistance value smaller.

In view of the above, in the third embodiment, it was studied how thevariation of the general term α_(k) influences the resistance variationratio at the time of cutting of a trimming line.

In this study, precursors of Examples 1-5 and Comparative Examples 1-4were prepared. The precursor of Example 1 is the same as that of Exampleof the first embodiment. The precursor of Example 2 is the same as thatof Example of the second embodiment. The precursors of ComparativeExamples 1 and 2 are the same as those of Comparative Examples 1 and 2for the first embodiment. Therefore, in Examples 1 and 2 and ComparativeExamples 1 and 2, the variation of the general term α_(k) is not takeninto consideration.

The precursors of Examples 3-5 were prepared as precursors that areconfigured substantially in the same manner as the precursor 70according to the first or second embodiment except for the trimminglines. Whereas the precursor 70 according to the first or secondembodiment has the six trimming lines, the precursors of Examples 3 and4 have eight trimming lines and the precursors of Example 5 has 10trimming lines.

In Example 3, the common ratio of the general term α_(k) of Inequality(1) of the geometric sequence described in the first embodiment is setat 0.59. In Examples 4 and 5, it is assumed that the general term α_(k)satisfies Equation (2) described in the second embodiment.

The precursors of Examples 3-5 are configured so as to be able to betrimmed by the trimming apparatus described in the first embodimentaccording to the flowchart of FIGS. 5 and 6.

The precursors of Comparative Examples 3 and 4 are configured in thesame manners as those of Comparative Examples 1 and 2 for the firstembodiment.

However, in Comparative Example 3, the common ratio of the general termα_(k) of Inequality (1) of the geometric sequence described in the firstembodiment is set at 0.50. The precursor of Comparative Example 3 isconfigured so as to be able to be trimmed by the trimming apparatusdescribed in the first embodiment according to the flowchart of FIGS. 5and 6.

In Comparative Example 4, as in the case of Comparative Example 3, thecommon ratio of the general term α_(k) of Inequality (1) of thegeometric sequence described in the first embodiment is set at 0.50. Theprecursor of Comparative Example 4 is configured so as to be able to betrimmed by the trimming apparatus described in the first embodimentaccording to the flowchart of FIG. 7.

In Examples 3-5 and Comparative Examples 3 and 4, as in the case of thefirst embodiment, the target resistance value Ra was set at 200Ω and thelower limit value Rb of the initial resistance value was set at 133.3Ω.

The precursors of Examples 3-5 and Comparative Example 3 were trimmed bythe trimming apparatus described in the first embodiment according tothe flowchart of FIGS. 5 and 6, and the precursor of Comparative Example4 was trimmed by the trimming apparatus described in the firstembodiment according to the flowchart of FIG. 7. Results are shown in atable of FIG. 20.

In this table, as described in the first embodiment, the term“resistance variation ratio at the time of cutting of a trimmingportion” means a ratio of a post-cutting resistance value to apre-cutting resistance value (i.e., initial resistance value ) In thethird embodiment, the variation range of α_(k) described in the firstembodiment is taken into consideration. More specifically, in the thirdembodiment, α_(k) is redefined as an average of plural α_(k)'s. Forexample, taking a variation range of α₁ as described in the firstembodiment, α₁ as used in the third embodiment is an average of pluralα₁'s.

In the table of FIG. 20, to prevent a post-trimming resistance valuefrom exceeding the target resistance value Ra, a value obtained byadding 3σ_(k) to α_(k) as used in the third embodiment is employedinstead of α_(k) as used in the third embodiment in determining trimminglines to be cut, where σ_(k) means the standard deviation of α_(k) asused in the third embodiment.

In the table of FIG. 20, a value obtained by subtracting 3σ_(k) fromα_(k) as used in the third embodiment is employed for every trimmingline as an example corresponding to a value close to the minimum valueof the variation range of α_(k) as used in the third embodiment.

It is therefore understood that the variation of the general term α_(k)is taken into consideration in Examples 3-5 and Comparative Examples 3and 4.

FIGS. 21-25 are graphs which are based on the table of FIG. 20 and showrelationships between the pre-trimming resistance value (i.e., initialresistance value) and the post-trimming resistance value in Examples 3-5and Comparative Examples 3 and 4.

FIG. 21 is a graph corresponding to Example 3, FIG. 22 is a graphcorresponding to Example 4, FIG. 23 is a graph corresponding to Example5, FIG. 24 is a graph corresponding to Comparative Example 3, and FIG.25 is a graph corresponding to Comparative Example 4.

Among these graphs, compare the graph of FIG. 21 (corresponds to Example3) with the graph of FIG. 9 (corresponds to Example 1) described in thefirst embodiment. As is understood from the description of the firstembodiment, the graph of FIG. 9 shows that the resistance value can befit into the target range with an assumption that the variation of thegeneral term α_(k) is not taken into consideration.

In contrast, the graph of FIG. 21 shows that the resistance value can befit into the target range even in the case where the variation of thegeneral term α_(k) is taken into consideration.

Compare the graph of FIG. 22 (corresponds to Example 4) and the graph ofFIG. 23 (corresponds to Example 5) with the graph of FIG. 19(corresponds to Example 2) described in the second embodiment. As isunderstood from the description of the second embodiment, the graph ofFIG. 19 shows that the resistance value can be fit into the target rangewith an assumption that the variation of the general term α_(k) is nottaken into consideration.

In contrast, the graphs of FIGS. 22 and 23 show that the resistancevalue can be fit into the target range even in the case where thevariation of the general term α_(k) is taken into consideration.

In the graph of FIG. 23, the variation of the post-trimming resistancevalue is smaller than in the graph of FIG. 22, which is because thenumber (10) of trimming lines in Example 5is larger than the number(eight) of trimming lines in Example 1. This indicates that theresistance value can be fit into the target range more easily as thenumber of trimming lines increases.

Compare the graph of FIG. 24 (corresponds to Comparative Example 3) withthe graph of FIG. 11 (corresponds to Comparative Example 2) described inthe first embodiment. The graph of FIG. 11 shows that as described inthe first embodiment the post-trimming resistance value varies to alarge extent with the initial resistance value and hence the resistancevalue cannot be fit into the target range, though it is assumed that thevariation of the general term α_(k) is not taken into consideration.

In contrast, in the graph of FIG. 24, since the variation of the generalterm α_(k) is taken into consideration, the post-trimming resistancevalue varies with the initial resistance value a little more than in thegraph of FIG. 11. Therefore, it is more difficult to fit the resistancevalue into the target range.

Compare the graph of FIG. 25 (corresponds to Comparative Example 4) withthe graph of FIG. 10 (corresponds to Comparative Example 1) described inthe first embodiment. The graph of FIG. 10 shows that as is understoodfrom the description of the first embodiment the post-trimmingresistance value can be fit into the target range with an assumptionthat the variation of the general term α_(k) is not taken intoconsideration.

In contrast, in the graph of FIG. 25, since the variation of the generalterm α_(k) is taken into consideration, the post-trimming resistancevalue varies to a large extent with the initial resistance value.Therefore, since the general term α_(k) actually has a variation, theremay occur a case that the resistance value cannot be fit into the targetrange.

Compare the graph of FIG. 25 (corresponds to Comparative Example 4) withthe graphs of FIGS. 21 and 22 (correspond to Example 3 and Example 4) todiscuss the graph of FIG. 25 further. In the graph of FIG. 25 thepost-trimming resistance value is smaller than in the graphs of FIGS. 21and 22 in a range where the initial resistance value is small. This isbecause variations of the resistance variation ratios of trimming linesaccumulate rather than cancel out each other. In addition, theresistance adjustment accuracy is not increased much even if trimminglines with small resistance variation ratios are provided by increasingthe number of trimming lines.

As is apparent from the above description, in Examples 3-5 of the thirdembodiment, the resistance value can be fit into the target range evenif the variation of the general term α_(k) is taken into consideration.This means that the result is the same even if the variation of thegeneral term α_(k) is not taken into consideration as in Example of thefirst or second embodiment.

This will be explained below in other words. As described in the firstor second embodiment, every time one trimming line is cut or left uncut,the resistance value of the resistance patterns 71 is measured andwhether to cut the next trimming line is determined on the basis of thethreshold value (β_(k)) therefor. Therefore, aresistance-element-dependent resistance variation ratio at the time ofcutting of a trimming line, that is, a resistance-element-dependentvariation of the general term α_(k), is absorbed. As a result, even onlywith the trimming adjustment, the resistance value can be fit into thetarget range with relatively high accuracy.

Even where the variation of the general term α_(k) should be taken intoconsideration as in the case of the third embodiment, the post-trimmingresistance value distribution range can be made narrower as the numberof trimming lines is increased according to a prescribed rule, that is,as trimming lines with smaller resistance value variations are provided.

Therefore, where a ladder-shaped resistance pattern is used, it need notbe trimmed. And analog trimming becomes unnecessary or trimmingadjustment amounts can be reduced. As a result, resistance elements areminiaturized, the trimming processing time can be shortened, andresistance value errors can be reduced. These advantages lead to costreduction, increase in production yield, and increase in thermalresponse speed. In the other points, the configuration and the workingsand advantages are the same as those of the first or second embodiment.

The invention is not limited to the above embodiments and can bepracticed in the form of the following various modifications:

(1) The resistor element is not limited to the platinum resistor 20 madeof platinum of a temperature sensor. A resistor element that is aresistor or the like made of any of various resistor materials may beformed on the front surface 11 of the substrate 10. In this case, thesame workings and advantages as attained by one of the above embodimentscan be attained by forming a precursor 70 as described in the oneembodiment as a precursor of the resistor element.

(2) The shape of the resistor pattern of the precursor 70 is not limitedto the shape described in each embodiment. Satisfactory results areobtained as long as a meandering resistor pattern is employed.

(3) The shape of each trimming line is not limited to a linear shape.Satisfactory results are obtained as long as each trimming line isshaped so as to short-circuit a corresponding one of pairs ofintermediate portions of the precursor 70.

(4) In general, satisfactory results are obtained as long as eachtrimming line is a short-circuiting portion for short-circuiting acorresponding one of pairs of intermediate portions of the precursor 70.

(5) The resistance value of the precursor 70 may be fit into a truetarget value by setting a target value smaller than the true one andtrimming a ladder-shaped pattern or an analog trimming pattern portionprovided in the precursor in advance at the end of a trimming operationon the precursor.

(6) Whether to cut a trimming line may be judged by judging whether apre-trimming resistance value is smaller than or equal to a thresholdvalue instead of judging whether the pre-trimming resistance value issmaller than the threshold value.

The invention has been described in detail by using the particularembodiments. However, it is apparent to a person skilled in the art thatvarious changes and modifications are possible without departing fromthe spirit and scope of the invention.

This application is based on Japanese Patent Application No.2004-147812, filed May 18, 2004, the disclosure of which is incorporatedby reference herein.

1. (canceled)
 2. A precursor having a resistance pattern which is formedon a substrate with a resistance material in meandering form andshort-circuiting portions which are formed so as to short-circuit pluralpairs of longitudinal intermediate portions of the resistance pattern,respectively, characterized in: that a normalized resistance valueincrease sequence obtained by arranging, in descending order, resistancevalue increases at the time of cutting of the respectiveshort-circuiting portions and normalizing the resistance value increasesby a resistance value obtained in a state that none of theshort-circuiting portions are cut is a sequence which has terms α_(k)'s(k=1, 2, 3, . . . ) and satisfies (1+α₁+α₂+ . . .+α_(k))(1+α_(k))=(1+α₁)².
 3. (canceled)
 4. A precursor resistance valueadjusting method in which a precursor having a resistance pattern whichis formed on a substrate with a resistance material in meandering formand short-circuiting portions which are formed so as to short-circuitplural pairs of longitudinal intermediate portions of the resistancepattern, respectively, is prepared and a resistance value of theprecursor is adjusted to a target resistance value by selectivelycutting the short-circuiting portions, characterized in: that theprecursor is prepared as a precursor in which a normalized resistancevalue increase sequence obtained by arranging, in descending order,resistance value increases at the time of cutting of the respectiveshort-circuiting portions and normalizing the resistance value increasesby a resistance value obtained in a state that none of theshort-circuiting portions are cut is defined as a sequence which hasterms α_(k)'s (k=1, 2, 3, . . . ) and satisfies (1+α₁+α₂+ . . .+α_(k))(1+α_(k))=(1+α₁)²; and that the resistance value of the precursoris adjusted to the target resistance value by repeating, in descendingorder of the cutting-induced resistance value increases of theshort-circuiting portions of the thus-prepared precursor, processing of:a first step of judging whether a resistance value of the precursorbefore cutting of the short-circuiting portion is smaller than athreshold value for the short-circuiting portion; a second step ofdetermining that the short-circuiting portion should be cut, if thefirst step judges that the resistance value of the precursor beforecutting of the short-circuiting portion is smaller than the thresholdvalue for the short-circuiting portion; and a step of judging, at thefirst step, skipping the second step, whether the resistance value ofthe precursor is smaller than a threshold value for a nextshort-circuiting portion whose cutting-induced resistance value increaseis largest next to the cutting-induced resistance value increase of thecurrent short-circuiting portion, if the first step judges that theresistance value of the precursor before cutting of the short-circuitingportion is larger than or equal to the threshold value for theshort-circuiting portion; while cutting the short-circuiting portionevery time the second step judges that the short-circuiting portionshould be cut, as the processing is repeated.
 5. (canceled)
 6. Aresistance element which is produced from a precursor by preparing aprecursor having a resistance pattern which is formed on a substratewith a resistance material in meandering form and short-circuitingportions which are formed so as to short-circuit plural pairs oflongitudinal intermediate portions of the resistance pattern,respectively, and adjusting a resistance value of the precursor to atarget resistance value by selectively cutting the short-circuitingportions, characterized in: that the precursor is such that a normalizedresistance value increase sequence obtained by arranging, in descendingorder, resistance value increases at the time of cutting of therespective short-circuiting portions and normalizing the resistancevalue increases by a resistance value obtained in a state that none ofthe short-circuiting portions are cut is defined as a sequence which hasterms α_(k)'s (k=1, 2, 3, . . . ) and satisfies (1+α₁+α₂+ . . .+α_(k))(1+α_(k))=(1+α₁)²; and that the resistance element is producedfrom the precursor by adjusting the resistance value of the precursor tothe target resistance value by repeating, in descending order of thecutting-induced resistance value increases of the short-circuitingportions of the precursor, processing of cutting the short-circuitingportion if the resistance value of the precursor before cutting of theshort-circuiting portion is smaller than a threshold value for theshort-circuiting portion, leaving the short-circuiting portion uncut ifthe resistance value of the precursor before cutting of theshort-circuiting portion is larger than or equal to the threshold valuefor the short-circuiting portion, and, with the current short-circuitingportion left uncut, cutting a next short-circuiting portion whosecutting-induced resistance value increase is largest next to thecutting-induced resistance value of the current short-circuiting portionif the resistance value of the precursor before cutting of the nextshort-circuiting portion is smaller than a threshold value for the nextshort-circuiting portion or leaving the next short-circuiting portionuncut if the resistance value of the precursor before cutting of thenext short-circuiting portion is larger than or equal to the thresholdvalue for the next short-circuiting portion.